Recently S. D. Cohen resolved a conjecture of Chowla and Zassenhaus (1968) in the affirmative by showing that, if f(x) and g(x) are integral polynomials of degree n ≥ 2 and p is a prime exceeding (n2 - 3n + 4)2 for which f and g are both permutation polynomials of the finite field Fp, then their difference h = f - g cannot be such that h(x) = ex for some integer c not divisible by p. In this note we provide a significant generalization by proving that, if h is not a constant in Fp and t is the degree of h, then and, provided t and n are not relatively prime. In a sense this measures the isolation of permutation polynomials of the same degree over large finite prime fields.
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics